Reservoir modeling is the process of building a digital representation of a reservoir that incorporates all characteristics pertaining to its ability to store and produce hydrocarbons. Reservoir models are subdivided into static and dynamic components. Static models are fine-scale simulations of rock properties such as porosity, permeability, capillary pressure, fractures, faults, seismic attributes, and parameters that do not change significantly with time. Dynamic models are coarser simulations that incorporate fluid properties that change with time, such as pressure and flow rates of oil, gas, and water.
Reservoir modeling covers at least 12 orders of magnitude, ranging from pore (nm to micron) to borehole (mm to m) to interwell (10's to 100's of m) to full-field scale (10's of km). Reservoir rocks are complex and heterogeneous at all scales. Multiscale simulation is a major goal of the petroleum industry, and many upscaling approaches have been proposed. See, e.g. Christie, M. A., 1996, Upscaling for reservoir simulation: JPT, v. 48, No. 11, p. 1004-1010 (hereinafter “Christie 1996”); and Durlofsky, L. J., 2003, Upscaling of geocellular models for reservoir flow simulation: A review of recent progress: 7th International Forum on Reservoir Simulation, Buhl/Baden-Baden, Germany, June 23-27, p. 58 (hereinafter “Durlofsky 2003”). Most of these conventional upscaling approaches start with fine-scale reservoir models that are coarsened to a model that typical fluid flow simulators can handle. The biggest challenge in this type of upscaling occurs because it is commonly difficult to preserve essential geologic heterogeneities in the resulting coarse models.
Heterogeneity can be defined as the variation in rock properties as a function of location within a reservoir or formation. Many reservoirs are heterogeneous because mineralogy, grain type and size, depositional environment, porosity, permeability, natural fractures, faults, channels, and other attributes vary from place to place. Heterogeneity causes problems in formation evaluation and reservoir simulation because reservoirs occupy enormous volumes, but there is limited core and log control. For example, a typical grid block used in a reservoir simulator is 250 m×250 m×1 m, borehole-scale numerical pseudocores represent rock volumes on the cubic-meter scale, and core plugs and microCTscans or confocal scans represent even smaller volumes.
A geocellular model is a layered, gridded 3D model. Layers can have zero thickness, as in the case of bed pinch outs or truncations. Layers can be as thin as the spacing of log measurements, or they can be thicker, to reflect the known thickness of rock layers. Geocellular models capture geologic-scale heterogeneities, and commonly have millions of cells.
Upscaling is the process of converting rock properties from fine scales to coarser scales. Upscaling algorithms assign suitable values of porosity, permeability, and other flow functions to each coarser grid block. See, Lasseter, T. J., Waggoner, J. R., and Lake, L. W., 1986, Reservoir heterogeneities and their influence on ultimate recovery, in Lake, L. W., and Carroll, H. B., Jr., eds., Reservoir Characterization: Academic Press, Orlando, Fla., p. 545-559 (hereinafter “Lasseter 1986”); Christie 1996; and Durlofsky 2003. Upscaling is necessary because reservoir simulators cannot handle the large number of cells in typical geocellular models.
There have been many upscaling attempts in reservoir simulation. Common approaches are summarized in: Lasseter 1986, Christie 1996, and Durlofsky 2003. A number of authors have used multi-point statistics (MPS) and representative element volume (REV) concepts in digital rock modeling. Okabe and Blunt (2004, 2005, 2007) used MPS to generate 3D pore systems from 2D thin sections. See, Okabe, H., and Blunt, M. J., 2004, Prediction of permeability for porous media reconstructed using multiple-point statistics: Physical Review E, v. 70, 10 p; Okabe, H., and Blunt, M. J., 2005, Pore space reconstruction using multiple-point statistics: Journal of Petroleum Science and Engineering, v. 46, p. 121-137; and Okabe, H., and Blunt, M. J., 2007, Pore space reconstruction of vuggy carbonates using microtomography and multiple-point statistics: Water Resources Research, v. 43. These authors assume that the 2D horizontal view was the same as the 2D vertical view, and proceeded to generate their model. Because of this assumption, their model does not capture rock heterogeneity, and does not depict true 3D pore geometry. MPS has been used to model carbonate facies tracts. See, Harris, P. M., 2009, Delineating and quantifying depositional facies patterns in carbonate reservoirs: Insight from modern analogs: AAPG Bulletin, v. 94, p. 61-86. MPS has been used to generate borehole-scale numerical rock models. See, Zhang, T., Hurley, N. F., and Zhao, W., 2009, Numerical modeling of heterogeneous carbonates and multi-scale dynamics: Presented at the SPWLA 50th Annual Logging Symposium, The Woodlands, Tex., June 21-24 (hereinafter “Zhang 2009”). Concepts of representative element volume (REV) and area (REA) have been applied to an outcrop photo of heterolithic sediments. See, Norris, R. J., and Lewis, J. J. M., 1991, The geological modeling of effective permeability in complex heterolithic facies: SPE Preprint 22692, Presented at the 66th Annual Technical Conference and Exhibition, Dallas, Tex., October 6-9, p. 359-374. REV has been discussed in relation to work with permeabilities in outcrop blocks of heterolithic sediments. See, Jackson, M. D., Muggeridge, A. H., Yoshida, S., and Johnson, H. D., 2003, Upscaling permeability measurements within complex heterolithic tidal sandstones: Mathematical Geology, v. 35, p. 499-520; and Jackson, M. D., Yoshida, S., Muggeridge, A. H., and Johnson, H. D., 2005, Three-dimensional reservoir characterization and flow simulation of heterolithic tidal sandstones: AAPG Bulletin, v. 89, p. 507-528. The concept of REV has been used in pore-scale digital rock models. However, because they used overlapping sub-volumes, they obtained questionable results. See, Zhang, D., Zhang, R., Chen, S., Soll, W. E., 2000, Pore scale study of flow in porous media: Scale dependency, REV, and statistical REV: Geophysical Research Letters, v. 27, No. 8, p. 1195-1198; and Okabe, H., and Oseto, K., 2006, Pore-scale heterogeneity assessed by the lattice-Boltzmann method: International Symposium of the Soc. of Core Analysts, Trondheim, Norway, September 12-16, Paper SCA2006-44, 7 p. The minimized variance concept of REV has been used to coarsen (upscale) reservoir simulations. See, Qi, D., 2009, Upscaling theory and application techniques for reservoir simulation: Lambert Academic Publishing, Saarbrücken, Germany, 230 p. (hereinafter “Qi 2009”).
3D pore-scale models have been built using 2D thin sections, using an approach known as Markov Chain Monte Carlo simulation. See, Wu, K., Van Dijke, M. I. J., Couples, G. D., Jiang, Z., Ma, J., Sorbie, K. S., Crawford, J., Young, I., and Zhang, X., 2006, 3D stochastic modelling of heterogeneous porous media—Applications to reservoir rocks: Transport in Porous Media, v. 65, p. 443-467. Upscaling questions have been addressed by building composite pore models using thin section scans of different resolution. See, Wu, K., Ryazanov, A., van Dijke, M. I. J., Jiang, Z., Ma, J., Couples, G. D., and Sorbie, K. S., 2008, Validation of methods for multi-scale pore space reconstruction and their use in prediction of flow properties of carbonate: Paper SCA2008-34, International Symposium of the Society of Core Analysts, Abu Dhabi, October 29-November 2, 12 p., which states: “One possible approach is to refine the coarser scale 3D image to equivalent resolution as the finer scale and then combine these two structures with the same volume into a single model.” The finer scale image is “superimposed” on the coarser scale image to form an integrated structure. See, id.
U.S. Pat. No. 6,826,520 describes a method to upscale permeability using a Voronoi computational grid. U.S. Pat. No. 7,224,162 describes a method to estimate properties of a geologic formation, using well log data such as nuclear magnetic resonance, resistivity, and other logs. The method acquires directional formation property values and generates a directional property log. U.S. Pat. No. 7,783,462 describes a method to populate a three dimensional reservoir framework having a plurality of cells with one or more constant reservoir property values. U.S. Pat. No. 7,765,091 describes a multi-scale method for reservoir simulation using a finite-volume method.
U.S. Patent Application Publ. No. 2011-0004448 describes a method to build 3D digital models of porous media using reflected white-light and laser scanning confocal profilometry and multi-point statistics. U.S. Patent Application Publ. No. 2011-0004447 describes a method to build 3D digital models of porous media using transmitted laser scanning confocal microscopy and multi-point statistics. The pore-scale REV concept is also discussed. U.S. Patent Application Publ. No. 2009-0262603 describes a method to generate fullbore images from borehole images. U.S. Patent Application Publ. No. 2009-0259446 describes a method to generate numerical pseudocores from conventional CTscans and fullbore images using multi-point statistics.